Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Step 3: Logistic Growth with General Harvesting = 2P 20(1-2 Step 3: Logistic Growth with General Harvesting We now extend the model from step 2

Step 3: Logistic Growth with General Harvesting
image text in transcribed
= 2P 20(1-2 Step 3: Logistic Growth with General Harvesting We now extend the model from step 2 to the general case, where the fish are also being caught at a constant rate H fish per year. Then the model from step 2 is modified as dP -H. dt 200 (1) Sketch graphs of the dP/dt against P for each of the values H = 50, 75, 90. Mark the corresponding equilibrium solutions on each plot. (2) For each of the H values above, what is the range of the initial condition such that the fish population does not extinct eventually? How does this range change when H is increasing from 50 to 90? (3) (Bonus 0.5pts) What happens to the equilibrium solutions as the value H + 0 (H decreases to 0)? What is the significance of this in terms of the fish pond population dynamics? (4) (Bonus 0.5pts) What happens to the equilibrium solutions as the value H + 100 (H increase to 100)? What is the significance of this in terms of the fish pond population dynamics? (5) (Bonus 0.5pts) What happens to the equilibrium solutions when H > 100 ? What is the significance of this in terms of the fish pond population dynamics? (6) (Bonus 0.5pts) Based on your analysis above, recommend a harvest strategy to the fish farmer to ensure long-term survival of the fish population while maximize the harvest. = 2P 20(1-2 Step 3: Logistic Growth with General Harvesting We now extend the model from step 2 to the general case, where the fish are also being caught at a constant rate H fish per year. Then the model from step 2 is modified as dP -H. dt 200 (1) Sketch graphs of the dP/dt against P for each of the values H = 50, 75, 90. Mark the corresponding equilibrium solutions on each plot. (2) For each of the H values above, what is the range of the initial condition such that the fish population does not extinct eventually? How does this range change when H is increasing from 50 to 90? (3) (Bonus 0.5pts) What happens to the equilibrium solutions as the value H + 0 (H decreases to 0)? What is the significance of this in terms of the fish pond population dynamics? (4) (Bonus 0.5pts) What happens to the equilibrium solutions as the value H + 100 (H increase to 100)? What is the significance of this in terms of the fish pond population dynamics? (5) (Bonus 0.5pts) What happens to the equilibrium solutions when H > 100 ? What is the significance of this in terms of the fish pond population dynamics? (6) (Bonus 0.5pts) Based on your analysis above, recommend a harvest strategy to the fish farmer to ensure long-term survival of the fish population while maximize the harvest

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Financial Institutions And Markets

Authors: Jeff Madura

10th International Edition

0538482176, 9780538482172

More Books

Students also viewed these Finance questions

Question

Why is it important to use ratios to analyze financial statements?

Answered: 1 week ago

Question

=+d) Perform the ANOVA and report your conclusions.

Answered: 1 week ago